Find a particular solution to the nonhomogeneous differential equation y? ? +4y? +5y=? 10x+e^(? x).

yp=
find the most general solution to the associated homogeneous differential equation. use c1 and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2.

yh=
find the most general solution to the original nonhomogeneous differential equation. use c1 and c2 in your answer to denote arbitrary constants.

y=

A) Particular solution:

B) Homogeneous solution:

C) The most general solution is

Step-by-step explanation:

Given non homogeneous ODE is

To find homogeneous solution:

To find particular solution:

Substituting in (1)

Equating the coefficients

The general solution is

from (2) ad (3)

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2